This is easy to test so don't write me off just by the subject.

Can anyone give me the odds of rolling a pair of dice 57 times and NOT getting doubles? That is what happened in my GNU BG when only counting the opening roll.

I first noticed an anomaly because it seemed that my GNU BG was giving really crappy opening rolls...consistently. I'm aware these things are usually psychological and I suppose it could still be the case here...I am a novice at statistics and backgammon. But, I became so curious that I started writing down my first rolls.

Now I see that I don't get crappy first rolls, rather, I hardly every get doubles on my first roll. I've now been monitoring this and I've gotten 6 doubles on my opening play out of 125 games. That is averaging 1 in 21 not 1 in 6...hmmm.

So, am I misunderstanding the nature of statistics? Is 125 games enough to expect a near 1/6 ratio or is this just one of those reasonable runs of bad luck. Can someone else monitor this and see if they have similar findings? My GNU BG version is 1.05.000-mingw 32-Bit 20150725. My seed is 803903184 and my trials are 1296 (I have no idea what trials are). All of this was set in the default install.

I assume that you took into account that the first roll in a game cannot be a double, so you can only count the second or third roll of the game depending on who went first.

In a live match last weekend we rolled five doubles in a row on the first roll before we could get the game started

what do you mean by another? please point me to a previously uncovered "rolling bug"

A few years back, while playing Yum! with my girlfriend, we roll a (combined) double 8 times in a row before we could even start the game.

At first I thought that the OP may be unaware that the opening roll cannot be doubles by rule.

However, as he is reporting some doubles, this misunderstanding seems less likely.

Anyway, bot dice conspiracies don't get much traction here. Yes, rare events do happen, that is part of the game and the nature of randomness. GNU and XG dice are fair unless altered by the user, end of story.

The odds of getting a double 6 / 125 times is 0.00498%. That probability is misleading though, since if you win the starting roll, it can't be a double. Assuming you win half of the starting rolls (63), it's 4.466%. If you also consider situations where you roll fewer than 6 doubles in 63 tries, it's 8.175%.

Getting no doubles in 57/2 ~= 29 tries (again because it's your opening roll) is expected at 0.505%. Unlikely, but not as remote as you may think.

If you want to play around with these, use the BINOM.DIST function in Excel.

Ok, I feel really stupid! As all of you mentioned, I was measuring my own first roll whether I won the toss or the follow up. Did I already say REALLY STUPID. Just to give you all a laugh, I changed the roll algorithm to the web base .org version and then concluded the app was filtering doubles.

7NTXX, I understand your jumping from .004% to 4% by cutting the data set down to 63. I don't understand what you mean by, "If you also consider situations where you roll fewer than 6 doubles in 63 tries, it's 8.175%".

This is a great lesson in emotions based on a really bad data assumptions. Thanks for not calling me stupid when you probably should have!

Alpha Fish, I was referring to the rampant suspicions I found on my searches not to any actual found bugs. I am not a conspiracist and so was honestly confused by my data which is irrefutable - however badly interpreted. This is how the conspiracy theories are born, I suppose.

I meant P(6 doubles|63 rolls) + P(5|63) + ... + P(0|63) = 8.175%. Not as relevant to your particular question, but helps put the odds of these "unlikely" situations into better perspective.

Ah, I think I get the idea. Thanks for clarifying.

I'm going to continue monitoring my first rolls out of curiosity. My "new" assumption is that I should get ~16% doubles if I only count my first rolls that are followup to the computer winning the the first roll. Is this a valid assumption (so I don't make an ass of myself again)?

Thanks for your time!

Over a large enough sample size, yes.

Playing "live," with a real board and dice, gives you a refreshing reminder that rare sequences do occur. After recently rolling three 17-to-1 jokers back-to-back-to-back, I mentioned to my chouette partners that an inexperienced beginner might be suspicious of rigged dice if that happened online.

The odds of rolling three doublets in a row is (1/6) cubed, or 1/216. Heck, we roll more times than that in just about every session!